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9-12 Integrated Math 1 Unit 5 Lesson 7

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K-5 Math 6-8 Math •9-12 Math

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•Integrated Math 1 Integrated Math 2 Integrated Math 3

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Unit 1 Unit 2 Unit 3 Unit 4 •Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 •Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11

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Lesson 7

7.1 Warm-up 7.2 Activity 7.3 Activity Student Lesson Summary

Unit 5, Lesson 7

It’s All on the Line

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Integrated Math 1

7.1

Warm-up

The image shows line .

<p>Line, slope = -2 over 5, y intercept =-1. 1 comma-5 and 0 comma-1 plotted.</p>

Write an equation for the line that is perpendicular to and whose -intercept is . Graph this line.
Write an equation for the line that is parallel to and that passes through the point . Graph this line.

7.2

Activity

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

Silently read your card and think about what information you need to answer the question.
Ask your partner for the specific information that you need. “Can you tell me _____?”
Explain to your partner how you are using the information to solve the problem. “I need to know _____ because _____”

Continue to ask questions until you have enough information to solve the problem.
Once you have enough information, share the problem card with your partner, and solve the problem independently.
Read the data card, and discuss your reasoning.

If your teacher gives you the data card:

Silently read your card. Wait for your partner to ask for information.
Before telling your partner any information, ask, “Why do you need to know ?”
Listen to your partner’s reasoning, and ask clarifying questions. Give only information that is on your card. Do not figure out anything for your partner!

These steps may be repeated.
Once your partner has enough information to solve the problem, read the problem card, and solve the problem independently.
Share the data card, and discuss your reasoning.

<p>Lines that intersect. Line l, y intercept = 2, slope=2 over 3. Line r, y intercept = 4, slope = -1 over 2.</p>

7.3

Activity

Line is represented by the equation . Write an equation of the line perpendicular to , passing through . Call this line .
Write an equation of the line perpendicular to , passing through . Call this line .
What do you notice about lines and ? Does this always happen? Show or explain your answer.

Student Lesson Summary

We can use the concepts of parallel and perpendicular lines to write equations of lines. The image shows line .

<p>Line, y intercept = 2, slope =-3. Point -1 comma 5 plotted </p>

Suppose is the image of when it is rotated 90 degrees using as a center. What is an equation of line ?

The point is on line . The center of rotation does not move when a figure is rotated, so will also be on the image, line . Because line was rotated 90 degrees, lines and are perpendicular. Their slopes must be opposite reciprocals. The slope of line is -3, so the slope of is . Now substitute the slope and the point into point-slope form to get .

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